We propose a detailed numerical study of a self-reacting floating point absorber, resembling the Ocean Power Technologies device PB3 PowerBuoy, for a possible installation in the Adriatic Sea. A simplified model of the mentioned device, composed of a floater sliding along a reacting body, which supports the floater, is studied, reproducing and analysing the most complex nonlinear phenomena, such as the wave overtopping and the out-of-water motion of the floater. Three different sizes of the device have been simulated, each with three different masses of the floater, deriving the time evolution of the wave in the surrounding of the floater, its frequency dispersion and energy content, the generated exciting force, the wave overtopping over the floater, and the out-of-water motion of the floater. The results highlight that the linear response is favoured by small floater density and optimal floater thickness. Additionally, large-sized devices are characterized by linear, but dissipative, response, while the response of medium-sized devices is only apparently linear.